Neutron star (NS) merger ejecta offer a viable site for the production of heavy r-process elements with nuclear mass numbers A >140. The crucial role of fission recycling is responsible for the robustness of this site against many astrophysical uncertainties. Here, we introduce new improvements to our scission-point model, called SPY, to derive the fission fragment distribution for all neutron-rich fissioning nuclei of relevance in r-process calculations. These improvements include a phenomenological modification of the scission distance and a smoothing procedure of the distribution. Such corrections lead to a much better agreement with experimental fission yields. Those yields are also used to estimate the number of neutrons emitted by the excited fragments on the basis of different neutron evaporation models. Our new fission yields are extensively compared to those predicted by the so-called GEF model. The impact of fission on the r-process nucleosynthesis in binary neutron mergers is also reanalyzed. Two scenarios are considered, the first one with low initial electron fraction is subject to intense fission recycling, in contrast to the second one which includes weak interactions on nucleons. The various regions of the nuclear chart responsible for fission recycling during the neutron irradiation as well as after freeze-out are discussed. The contribution fission processes may have to the final abundance distribution is also studied in detail in the light of newly defined quantitative indicators describing the fission recycling, the fission seeds and the fission progenitors. In particular, those allow us to estimate the contribution of fission to the final abundance distribution stemming from specific heavy nuclei. Calculations obtained with SPY and GEF fission fragment distributions are compared for both r-process scenarios.